On the quality of red wine by Enrique Araujo

This dataset contains 1599 red wines alongside 11 variables that describe their chemical properties. It provides ratings on every one on a scale from 0 (very bad) to 10 (very excellent), agreed upon by no less than than 3 experts.

Univariate Plots Section

First, a look at the structure of the dataset:

## 'data.frame':    1599 obs. of  13 variables:
##  $ X                   : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ fixed.acidity       : num  7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
##  $ volatile.acidity    : num  0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
##  $ citric.acid         : num  0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
##  $ residual.sugar      : num  1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
##  $ chlorides           : num  0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
##  $ free.sulfur.dioxide : num  11 25 15 17 11 13 15 15 9 17 ...
##  $ total.sulfur.dioxide: num  34 67 54 60 34 40 59 21 18 102 ...
##  $ density             : num  0.998 0.997 0.997 0.998 0.998 ...
##  $ pH                  : num  3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
##  $ sulphates           : num  0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
##  $ alcohol             : num  9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
##  $ quality             : int  5 5 5 6 5 5 5 7 7 5 ...

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.000   5.000   6.000   5.636   6.000   8.000

The output variable of this dataset is the Quality. Most wines are middle of the pack when it comes to quality, rating 5-6. The minimum rating is a 3, while the maximum is 8. There are more high-rated wines than low-rated ones.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    4.60    7.10    7.90    8.32    9.20   15.90

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.1200  0.3900  0.5200  0.5278  0.6400  1.5800

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   0.090   0.260   0.271   0.420   1.000

On one hand, the distributions for the volatile and fixed acidity are both similar in that they’re right skewed and have a similar overall shape. Are they correlated to each other? On the other hand, the citric acid one is a bit more unique, with distinct peaks at 0 and 0.50.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.900   1.900   2.200   2.539   2.600  15.500

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.01200 0.07000 0.07900 0.08747 0.09000 0.61100

Looking at the residual sugar and chlorides (salts), both variables have similar right-skewed distributions. Most wines have quite similar values: between 2 and 3 for sugar, and 0.1 to 0.2 for chlorides.

Tranforming the scales gives a closer look.Since there are no 0 values I used a log10 transform on the x-axis. Like this, distributions are well behaved and have a clear mode. Since these two data had very noticeable outliers, I’m curious about the quality of the wines to which these belong to, especially the sweeter wines, so I’ll subset them:

I plotted the quality of wines that have more than 10 grams per liter of sugar. Not only do we have few fines that satisfy this condition, but their quality doesn’t go beyond a 6.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00    7.00   14.00   15.87   21.00   72.00

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    6.00   22.00   38.00   46.47   62.00  289.00

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.3300  0.5500  0.6200  0.6581  0.7300  2.0000

This next trio of variables have a similar pattern. They’re right-skewed, which means the majority of the wines have similar quantities of chemicals and there are a few outliers which drive the means up. Once again, I use a log-transform on the first two to get a closer look. For the sulphates, I limit the x-axis to show up to the 99th percentile.

With the transformation I see that the free and total SO2 distributions are not what the seemed to be. Data points are more interspersed in the lower values for the free SO2, with the mode being around 6, with another peak near 16. On the other hand, for the total SO2, values seem normally distributed on a log scale. The mode is between 40 and 50.

length(subset(mydata, free.sulfur.dioxide > 50))
## [1] 13

It is said that free sulfur dioxide, in concentrations of over 50ppm (mg/L), becomes evident in the nose and taste of wine. So I look at the quality of the 13 wines that go over this concentration.

Since there are few wines with high concentrations of free SO2 it’s difficult to draw conclusions. Nonetheless, it’s curious that these wines have scores of 5 to 7, as high concentrations can be seen as negatives beforehand. In this case it appears that it doesn’t have much of a negative impact, we even find that there are two wines with a score of 7.

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9901  0.9956  0.9968  0.9967  0.9978  1.0037

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.740   3.210   3.310   3.311   3.400   4.010

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.40    9.50   10.20   10.42   11.10   14.90

The final 3 variables. Density and pH are the first chemical variables to not be skewed. Density might not be that important to quality, by definition it’s mostly dependent on the concentration of other chemicals and has very little range (in g/ml):

max(mydata$density) - min(mydata$density)
## [1] 0.01362

Alcohol and pH, however, have much wider ranges and might have something to say about the flavor of the wine.

Univariate Analysis

What is the structure of your dataset?

There are 1599 wines in this dataset with 12 features:

  1. fixed acidity
  2. volatile acidity
  3. citric acid
  4. residual sugar
  5. chlorides
  6. free sulfur dioxide
  7. total sulfur dioxide
  8. density
  9. pH
  10. sulphates
  11. alcohol
  12. quality

All variables except for quality are decimal numbers which describe a chemical property of the wine. Quality is an integer between 0 and 10. Most wines have a quality of 5 or 6. Also, we don’t have any 9’s or 10’s in this data.

What is/are the main feature(s) of interest in your dataset?

The main feature of interest in this dataset is the quality of the wine. I’d like to learn which of the chemicals variables are most closely related to the taste and score.

What other features in the dataset do you think will help support your
investigation into your feature(s) of interest?

I think the most important features are the ones that are closely related to the taste, according to the dataset’s description. These variables are the volatile acidity, which if high can lead to an unpleasant vinegar-like taste; the citric acid concentration, which is said to be related to ‘freshness’ and flavor; the chlorides, which is the concentration of salts; and the sulphates, which are an additive that controls microbial growth and affects the SO2 concentration, affecting taste indirectly.

Did you create any new variables from existing variables in the dataset?

I did not create any new variables during the past section.

Of the features you investigated, were there any unusual distributions?
Did you perform any operations on the data to tidy, adjust, or change the form
of the data? If so, why did you do this?

Most distributions were right-skewed, and some variables, like sulphates, chlorides and residual sugar, had more outliers than the others. The citric acid distribution has two spikes, one at zero and one near 0.5. However I did not see the need to change the form of the data or use log scales in the histograms.

Bivariate Plots Section

First, since I have so many variables with long names, I create a plot with the correlation ellipses between them. Already we see some strong relationships. Some are expected, like pH being more acidic on wines with more citric acids and fixed acidity. And some are curious, like the one relationship between alcohol and quality.

Since I’m looking at quality as the main output feature, I’ll look into the variables with the most correlation next, beginning with the positive.

These are the variables with the most positive correlation to the quality. Still, it’s a moderate correlation at best. Now, for the negatively correlated ones.

According to the dataset’s descriptions, some variables with considerable correlation do affect the flavor of the wine directly:

The other two, alcohol and sulphates, have different effects. Alcohol is alcohol, while the sulphates help preserve the freshness by preventing oxidation. This means the sulphates are related to a wine’s shelf life.

Next, for a deeper look at the variables, I group them by the quality of the wine to see how they vary.

This box-plot showcases how different are the higher rated wines from the poor ones. In terms of volatile acidity, most of the wines rated 7 or 8 have less than 0.5g/L of acetic acid. Poor rated wines, on the contrary, have a concentration of more than 0.6g/L. This is in line with the descriptions, poorly rated wines have unpleasant taste.

Next up is the concentration of citric acid. In this one the most noticeable feature is the variance, which is large for ratings 3 to 6, but small for wines rated 7-8. Most top rated wines have more than 0.3g/L of citric acid. There is a moderate, positive relationship between this and the flavor. Critics tend to like wines with more citric acid, although is not the only factor.

Now this one is a relationship I didn’t not expect, yet the data shows that it’s not by mere chance. Many top rated wines are firmly above the 11% mark, while the worst ones (rated 3) are below it. Surely, having more alcohol does not make a better wine, but the worse wines have little of it.

Finally, the concentration of sulphates. High-rated wines tend to have more sulphates in a tendency similar to the last two variables. It’s hard to relate this variable to the wine’s flavor without taking into account its shelf life. It could be that the poorer wine’s taste worsens quicker.

Now, looking outside of quality, I see other strong relationships, like pH and fixed acidity, and alcohol and density. These have very clear scientific explanations, but nonetheless it’ll be interesting to take a look at them in plots.

First, the acidity. More acids lower the pH, as is expected, and that shows in the r values for these two variables. Of course, pH is also affected by other variables, like citric acid concentration and alcohol percentage. This shows in the variability of the points in this plot.

Next up, alcohol and density. Because, alcohol is less dense than water (density = 1), more alcohol content means less density, which explains the correlation. However, much like in the pH’s case, other variables have an effect on the density, since they are the concentration of chemicals present in the wine. I think it’s safe to say many of the chemical variables are correlated in one way or another.

Bivariate Analysis

Talk about some of the relationships you observed in this part of the
investigation. How did the feature(s) of interest vary with other features in
the dataset?

The quality of a wine varies a bit with other features, such as the concentration of citric acid, sulphates and acetic acid (volatile acidity), and also has a moderate correlation with the alcohol percentage. All these relationships are weak, however, between coefficients of 0.2 and 0.4.

Did you observe any interesting relationships between the other features
(not the main feature(s) of interest)?

The relationships between the other variables have clear scientific foundations yet are interesting to see. The concentration of acids (citric, acetic) have a clear effect on the density and pH; more acids, more density and lower pH. Alcohol is also related like this, as wines with more alcoholic content tend to have lower pH and less density, as is expected.

What was the strongest relationship you found?

The strongest relationship according to Pearson’s coefficient is pH and fixed acidity, with a value of -0.6829. This means the concentration of tartaric acid explains at least 68% of the variation in pH across our wine data.

Multivariate Plots Section

These density plots expand upon the relationships showcased in the previous boxplots. These 4 variables are the ones with the strongest correlation to the quality, and in these plots we can see the attributes of the best wines more clearly.

The two chemical quantities that stand out the most are sulphates and volatile acidity. The majority of high quality wines (rated 7-8) are on a class apart from the rest: they have more sulphates and less acetic acid (volatile acidity) and it clearly shows in the density plots.

The other two variables, citric acid and alcohol, don’t show clear differences. In addition, it’s important the ranges of these distributions. Higher quality wines tend to have distinct quantities of chemicals, yet there are some high quality wines that have few sulphates or citric acid, or somewhat elevated volatile acidity.

Now, to look further into these relationships, I plot two variables against each other on a scatter plot, coloring each point by the wine’s quality. In this first one I pitted the volatile acidity against the sulfate concentration. Data points are very scattered but there is a noticeable pattern in there. Since the higher values are outliers, I use a log transform in the x-axis.

Faceting this scatter plot makes us appreciate how little data we have for wines rated 3 and 8. We can a moderate relationship between these variables: worse wines are up to the left, while the better ones are centered in the plot. This time I use a log transform for the sulphates, and a square root transform for the citric acid, which has 0 values.

My second plot has citric acid vs sulphates. These two have moderate positive correlation to quality, so it’s expected that higher values for each means a better wine. However, we see a lot of variation in here as fell. Once again, I use a log transform for the x-axis and square root for y-axis.

Finally, I compare two acids, citric vs acetic. One is related with fresh taste, the other with a bad, vinegar-like one. Once again, there is a lot of variance.

CV + facet_wrap(~cut(sulphates, c(0,0.5,0.6,0.7,0.8,0.9,2))) +
  scale_color_brewer(palette = "Reds") +
  labs(title = "Citric acid vs volatile acidity (faceted)")

In an effort to integrate another variable into this scatterplot, I tried faceting by the amount of sulphates. I defined bins that tried to divide the data points into something that made sense. The result shows how the majority of wines, which are rated 5-6, are in the first 3 bins, from 0 to 0.7 g/L of potassium sulphate. The next two bins are dominated by the better wines, and the final one is filled with outliers and has wines of every rating.

Multivariate Analysis

Talk about some of the relationships you observed in this part of the
investigation. Were there features that strengthened each other in terms of
looking at your feature(s) of interest?

First, the volatile acidity is bad for the taste when it’s high, so poorer wines tend to hang out in the upper values. The sulphates appear to have a positive relationship with quality, and the best wines are centered around a value of 0.8, yet with high variance.

Wines rated 8 points can have little citric acid or a lot. There seems to be a ‘sweet spot’ in which the high quality wines are, as too much citric acid seems to be disliked.

Comparing citric and acetic acid, the best wines tend to have little volatile acidity and a good amount of citric acid. It appears there’s a weak negative correlation between these two. Note that the worse wines tend to have more acetic acid, yet there are some outliers within the high scores that do too.

Were there any interesting or surprising interactions between features?

I’m most surprised at how there is so much variance in the data. It’s easy to find where the bad ones will be, but the good ones appear all over the plots. Since the correlations are not that strong, it’s very difficult to build a model that can predict the score by looking a these variables. If I did build one, I’d certainly expect it to be better at classifying bad wines. There are many outliers, it’s possible to find a bad wine that has two or three properties on the same level as a good one.

Final Plots and Summary

Plot One

Description One

The distribution of the concentration of citric acid is the most unique one. It has these spikes at 0 and 0.5 g/L while being otherwise unremarkable. As the presence of citric acid is desirable, the density plots per wine quality gives an alternate view of this distribution, and show that most of the wines with no citric acid have poor taste. Wines rated 7 and 8 have a considerable number of samples with concentrations around 0.5g/L.

Plot Two

Description Two

Volatile acidity, also known as the concentration of acetic acid, is the variable that has the strongest negative correlation with quality. Too much acetic acid can make for very bad taste. The boxplot and the density plot we did for this variable showcased this relationship well, so the violin plot is a nice combination of the two. The best wines have a distribution that leans towards low quantities of acetic acid. However, this quantity alone can’t determine how good a wine is.

Plot Three

Description Three

This plot highlights how difficult it can be to separate the best wines from the worst based on chemical qualities. The volatile acidity and the sulphates were two variables that, in density plots, separated the top wines more clearly. Yet, when put together in a scatterplot, the separation definitely isn’t as clear. Better wines appear to be a subset of the previous rating. There is no clear linear relationship between quality and other variables.

Reflection

This red wine dataset contained information on 1599 wines, with measurements for 11 chemical properties and one output variable: quality. I began by plotting the distributions of each variable, and then looked for relationships using pearson’s correlation coefficient. Once I had identified the most useful variables, I plotted two and three-variable graphics which could help visualize how they were related to the quality more effectively.

To my surprise, there wasn’t a clear-cut relationship between the many chemical properties and a wine’s quality. Nowhere I could draw a line and say “that’s it, from this point on there are only high quality wines”. In spite of this, I managed to observe some interesting relationships, like the ones between sulphates and citric acid with a wine’s quality.

I think the main limitation of this dataset lies in the quantity of observations. There are 1599 wines, yet too few of them are rated 3 or 8, and we even lack wines rated more than 8, or less than 3. Correlations are moderate at best, so it’s difficult to build models that predict a wine’s quality according to these variables. I feel that with more data points, a reliable, more complex model can be built, perhaps with some machine learning algorithm.